Polynomial-based Filters Research Articles

Comparative performance of some polynomial-based lowpass filters for microwave/digital transmission applications

ABSTRACTThis paper reports on the comparative performances of some polynomial based lowpass filters in the lumped elements, microstrip and defected ground structure (DGS) environment. The microwave designers are normally familiar with Butterworth, Chebyshev and Bessel filters. However, many more polynomials based, ripple and non-ripple types LPF have been suggested for the low-frequency applications. Some of these LPF, such as L-opt, H-type, Transitional Butterworth-Legendre (TBL), Pascal, Legendre group of LPF, are compared for their applications in analog microwaves, digital transmission, efficiency enhancement of the linear power amplifiers and five level partial response modulations. A method is reported to compute the ripple frequency for the Legendre group of LPF and Pascal LPF. Further, a design is suggested to significantly improve group delay performance of high selectivity filters.

Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure

Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP) to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.

Estimation of Length and Order of Polynomial-based Filter Implemented in the Form of Farrow Structure

Digital polynomial-based interpolation filters implemented using the Farrow structure are used in Digital Signal Processing (DSP) to calculate the signal between its discrete samples. The two basic design parameters for these filters are number of polynomial-segments defining the finite length of impulse response, and order of polynomials in each polynomial segment. The complexity of the implementation structure and the frequency domain performance depend on these two parameters. This contribution presents estimation formulae for length and polynomial order of polynomial-based filters for various types of requirements including attenuation in stopband, width of transitions band, deviation in passband, weighting in passband/stopband.

A Class of Wide-Band Linear-Phase FIR Differentiators Using a Two-Rate Approach and the Frequency-Response Masking Technique

This paper introduces a class of wide-band linear-phase finite-length impulse response (FIR) differentiators. It is based on two-rate and frequency-response masking techniques. It is shown how to use these techniques to obtain all four types of linear-phase FIR differentiators. Design examples demonstrate that differentiators in this class can achieve substantial savings in arithmetic complexity in comparison with conventional direct-form linear-phase FIR differentiators. The savings achievable depend on the bandwidth and increase with increasing bandwidth beyond the break-even points which are in the neighborhood of 90% (80%) of the whole bandwidth for Type II and III (Type I and IV) differentiators. The price to pay for the savings is a moderate increase in the delay and number of delay elements. Further, in terms of structural arithmetic operations, the proposed filters are comparable to filters based on piecewise-polynomial impulse responses. The advantage of the proposed filters is that they can be implemented using non-recursive structures as opposed to the polynomial-based filters which are implemented with recursive structures.

Polynomial-based filters with odd number of polynomial segments for interpolation

In many signal processing applications, it is beneficial to use polynomial-based interpolation filters. Actual implementations of these filters can be performed effectively by using the Farrow structure or its modifications. In the literature only polynomial-based filters having even number of polynomial pieces N have been considered. This letter presents a modification of the implementation form which allows realizing polynomial-based filters having an odd number of polynomial pieces. The condition that N must be even integer is not required any more. Further, a frequency-domain filter optimization method is developed, based on the methods for even-length filters. We illustrate through examples the performance of the odd-length polynomial-based filters.